I am super confused about this. I thought that for an entangled particle if you measure the spin of one, the whole system should get randomized (as both particles are inherently connected and the state of one has been measured). How do we know the unmeasured particle is actually the opposite spin? All the explanations I read is when we measure the spin of 1 particle we automatically know the spin of the entangled particle is opposite, but how can this be verified when measuring the spin of the first should have randomized the whole system? Without verification we can't get the "spooky action at a distance" phenomenon so there has to be a way to measure both particles and then compare their states but this doesn't make sense to me as measuring one should have randomized the other.
Measuring one quantum mechanical system doesn't randomize the system. The randomness becomes apparent only if an ensemble of measurements is done. Now the entangled system is one system. So every time you measure spin up of one particle you should measure spin down (or up, depending on the entanglement) of the other. And the other way round. If you make a huge number of measurements then the situation is randomized. Each pair of results will be observed in accordance with the superposition of the spins. If the entanglement is such that both states of spins are equally likely to be measured then you will find a 50/50 distribution of two different results (this is the randomization).